Interaction of high-frequency and low-frequency oscillations in the synchronized oscillator
DOI:
https://doi.org/10.3103/S0735272715120031Keywords:
synchronization, Van der Pol oscillator, three-frequency interactionAbstract
Theoretical analysis of the oscillation synchronization under conditions of simultaneous low-frequency and high-frequency external impact on the oscillator has been conducted using an example of the generalized Van der Pol oscillator. It was shown that the interaction of high-frequency and low-frequency oscillations resulted in the appearance of additional regions of synchronization as a result of three-frequency interaction between the frequencies of such interaction and the natural frequency of oscillator. For the case of three-frequency interaction, characteristics of synchronous oscillations were determined and compared with those for the case of primary tone synchronization of oscillator.References
ADLER, ROBERT. A study of locking phenomena in oscillators. Proc. IRE, Oct. 1973, v.61, n.10, p.1380-1385, DOI: http://dx.doi.org/10.1109/PROC.1973.9292.
BLEKHMAN, I.I. Synchronization in Nature and Technology. Moscow: Nauka, 1981 [in Russian].
LANDA, P.S. Self-Sustained Oscillations in Systems with a Finite Number of Degrees of Freedom. Moscow: Nauka, 1980 [in Russian].
PIKOVSKY, A.; ROSEMBLUM, M.; KURTHS, J. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge: CUP, 2001.
GONZÁLEZ–MIRANDA, J.M. Synchronization and Control of Chaos. An Introduction for Scientists and Engineers. Imperial College Press, 2004.
LAI, YI MING; PORTER, MASON A. Noise-induced synchronization, desynchronization, and clustering in globally coupled nonidentical oscillators. Phys. Rev. E, Jul. 2013, v.88, p.012905-9, DOI: http://dx.doi.org/10.1103/PhysRevE.88.012905.
BELOGORTSEV, A.B.; VAVRIV, D.M.; TRETYAKOV, O.A. Chaos in the quasilinear Van der Pol oscillator. Radiotekh. Elektron., 1990, v.35, n.6, p.1300-1307.
VAVRIV, D.M.; CHERNYSHEV, I.Y. Experimental study of stochastic instability of nonlinear oscillator. Radiotekh. Elektron., 1990, v.35, n.1, p.151-158.
BELOGORTSEV, A.B.; VAVRIV, D.M.; TRETYAKOV, O.A. Destruction of quasiperiodic oscillations in weakly nonlinear systems. Appl. Mech. Rev., 1993, v.46, n.7, p.372-384, DOI: http://dx.doi.org/10.1115/1.3120366.
MITROPOLSKII, Y.A. Nonstationary Processes in Nonlinear Oscillating Systems. Kiev: AN UkrSSR, 1955 [in Russian].
